DE2616141A1 - ELLIPSOMETRIC MEASURING METHOD - Google Patents

Description

Boeblingen, April 8, 1976 pr-fr

Applicant: International Business Machines

Corporation, Armonk, N.Y. 10504

Official file number: New registration

File number of the applicant: YO 974 065

Ellipsometric measuring method

The invention relates to an ellipsometric measuring method which is a linear or elliptically polarized monochromatic light beam with a known angle of incidence and with a known position its direction of polarization directed at a test object and after reflection on this one analyzer and one downstream Photo detector is fed.

In many areas of technology, for example in manufacture of integrated circuits, it is necessary to adjust the thickness and / or to determine the refractive index of very thin layers with high accuracy and high speed. In particular So-called ellipsometric methods have recently been used for the automatic measurement of the thickness of extremely thin layers proven particularly well. In these methods, a linearly or elliptically polarized beam is at a relatively large angle of incidence directed at a test object and the ellipticity of the reflected beam indicated by one in the course of this beam; ordered rotating analyzer and a downstream; eten photodetector determined. The pulses appearing at the output of the photodetector are digitized and at the same time as the Information on the occurrence of the individual values in each case

609846/0873

lying angular positions of the rotating analyzer of a processing unit fed. Such devices are described, for example, in German Offenlegungsschrift 2,430,521.

The values Δ and Ψ measured with these devices, where

The phase difference between the parallel and perpendicular components R and R of the electrical vector of the reflective

R.
th ray and tHiLÜ ^Ϋ = - is, enable the calculation

the thickness and the refractive index of the examined layer. the The high measurement accuracy achievable with the device mentioned is also due to the use of Fourier analysis in the evaluation the information appearing at the output of the photodetector traced back.

A disadvantage of the known devices is that between mutually complementary polarization states of the same orientation and ellipticity but opposite direction of rotation, ie left-directed and right-directed ellipticity ₍ cannot be distinguished. As a result, only the angle Ψ can be clearly determined, while when determining the phase angle Δ, ambiguities can occur. While the angle Ψ can only change between 0 and 90 ° and is therefore necessarily unique, the phase angle .Δν can assume values between 0 and 360 ° Known devices are avoided, but two measuring processes with different polarization directions of the measuring beam or additional information about the measuring object are required, which not only reduces the measuring speed but also causes additional sources of error.

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In the reference "Polarized Light and Optical Measurement by D. Clarke and J.F. Grainger, Pergamon, New York 1971, is referred to the combination of a retardation plate and an analyzer and referred to it as a polarimeter and shown that such a combination enables a complete determination of the polarization by a single measurement. Such a combination can consist of a rotating deceleration element arranged in front of a stationary analyzer exist. However, the above cited literature does not contain any Information on the use of such elements in ellipsometry.

The invention is based on the task of specifying a simple method and a device for carrying out this method, in which the ellipsometric parameter δ , ie the phase difference between the parallel and perpendicular components of a beam elliptically polarized by Refle.X-ion, is easier Way can be clearly determined.

Furthermore, it should be possible to unambiguously determine Δ with relatively little technical effort, at great speed and to be made possible by a single measurement process. This object is achieved by the method described in claim 1.

By arranging a rotating λ / 4 plate or a die element causing the same effect in the path of the reflected beam in front of an analyzer and by the Fourier analysis of the signals occurring at the output of the downstream photodetector can be used to measure the phase angle Δ by a single measurement process can be clearly identified. This advantage is due, among other things, to the fact that the Fourier coefficients contain both sinA and cosA terms, so that the sign of the phase angle Δ i.e. the direction of polarization of the

YO 974 065 6 0 ₉ 846 ~ 7ö8 7 3

elliptical polarization can be determined in an unambiguous way, what with the previously known devices in one Operation could not be carried out. In addition, by making available the term sin Δ, the measurement accuracy, especially for values of Δ for the cos Δ in the vicinity of 1 is very much increased.

The invention is based on FIGS. explained in more detail. Show it:

Fig. 1 is a schematic representation of a known

ellipsometric device.

Fig. 2 shows a section, including electrical

rule block diagrams, from the device shown in FIG.

3 is a schematic illustration for illustrative purposes

solution of the with the help of the in FIGS. 1 and the device shown .

Figs. 4 and 5 are schematic representations of exemplary embodiments the invention.

In the device shown in Fig. 1, for example, generates a light source 10 consisting of a 1-mW helium-neon laser a light beam penetrating a polarization prism 12 21. The polarization prism 12 is arranged so that the plane of polarization of the light beam 21 leaving it a has a fixed position, preferably 45 °, with respect to the plane of incidence of the light beam on the test object 20. The beam

YO 974 065 60 9K46 / 0B7 3

penetrates a λ / 4 plate before it hits the test object 14, which is also fixed at a predetermined and known angle, and then a diaphragm 18 for Determination of the light spot arising on the measurement object 20. The light beam 22 reflected on the test object is elliptically polarized and passes through an aperture diaphragm 24 and one continuously, for example rotating at 5 revolutions per second, preferably designed as a polarizing prism Analyzer 26, after which it strikes a photodetector 28, for example as a secondary electron multiplier can be formed. In Fig. 2 a section of the device shown in Fig. 1 is shown in more detail. In addition to the elements already shown in FIG. 1, the device shown in FIG. 2 contains an angle encoder which is connected to the rotating analyzer 26 and has two outputs

31 and 33 has. The device is designed in such a way that the encryptor 30 and the analyzer 26 are fastened together on a rotating hollow shaft. At the output 31, a signal occurs with each revolution of the analyzer 26, while at the output 33 signals occur for a plurality of equal partial revolutions of the analyzer. The signals appearing at output 33 are sent as trigger pulses to an analog-digital converter

32 supplied.

The signals appearing at an output 35 of the photodetector 28 designed as a secondary electron multiplier are used as Analog signals fed to an analog-to-digital converter 32 and have for example the shape shown in FIG. 2 by the line 34. In the analog-to-digital converter 32 this is from the secondary electron multiplier 28 is converted into a series of digital signals, for example those shown in Fig. have the shape indicated at 36. This digital signal is then designed as a small computer, for example Analyzing device 38 supplied, in which the digital values are subjected to a Fourier analysis to determine the individual Fourier coefficients to determine which latter is the ellipsometric

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26Ί6ΗΊ

Analysis of the reflected light are required. The full Fourier transform is not required. After determining the normalized coefficients of the second harmonic of the Fourier transform Ellipsometric formulas are evaluated in order to determine the optical properties of the test object to calculate the necessary parameters. The values of these parameters are either grounded, for example with the aid of a typewriter printed or made visible with the help of a cathode ray tube.

As indicated in FIG. 3, a Fourier numerical analysis of the digital waveform 36 is performed. In the case of the ellipsometer with a rotating analyzer, as described, for example, in the above-mentioned laid-open specification 2 430 521, the normalized Coefficients a ~, b «of the Fourier series are determined. The common ones ellipsometric formulas are used to calculate the desired Object parameters, for example layer thickness and refractive index. In Fig. 3 is also a printing device 40 and a device indicated for display 42. The information printed or displayed is azimuth angle α, ellipticity χ the ellipsometric parameters Ψ and Δ, film thickness, refractive index etc.

The Fourier analysis in the analyzing device 38 can be carried out with the aid of known programs.

In the device shown in Fig. 1, the polarizing Element 12 fastened in different positions v / earth so that the plane of polarization of the beam leaving this element with the plane of incidence angles of, for example, 0 °, 12 °, 45 ° and 90 ° includes.

YO 974 065 609846/087

In the exemplary embodiment of the invention shown in FIG. 4, elements corresponding to the elements shown in FIG. 1 are denoted by the same reference numerals. The monochromatic light beam 21 emanating from a light source 10. reaches to a fixed polarizer 12 and falls on the surface of a test object 20 at an angle φ. The polarizer 20 can, as indicated, for example, in the above-mentioned German laid-open specification 2 430 521, be fastened so that the azimuth of the plane of polarization of the linearly polarized beam leaving it can be set at different angles with respect to the plane of incidence. The reflected beam passes through a compensator 50 designed as an optical λ / 4 delay element, which preferably consists of a λ / 4 plate. The compensator is rotated at a constant angular velocity with the aid of means not shown. Its respective angular position is denoted by q. The light leaving the compensator is fed to a fixedly arranged analyzer 52 and then arrives at a secondary electron multiplier designed as a photodetector

j at the output 35 an electrical signal occurs, the one; Function of the intensity iUi transmitted by the analyzer 52 Is light.

j To illustrate and explain the method according to the invention the following exceptions are assumed:

The polarizer 12 is set in such a way that the polarization j ' plane of the linearly polarized beam leaving it encloses an angle of 45 ° with the plane of incidence. The direction of passage of the fixedly arranged analyzer 52 forms an angle of 0 ° with the plane of incidence. If it is also assumed that the fast axis of the compensator 50 forms an angle θ with the plane of incidence I at a given point in time,!

c ,

YO 974 065 609 84fi / 0

and that it is an ideal compensator, i.e. that the delay between the two transmission directions is exactly a quarter wavelength, then the intensity Ι (θ) ; of the incident on the secondary electron multiplier 28 Light is defined by the following relationship, taking into account a multiplicative constant:

I (θ) = A _n + A ₀ cos 2 θ + B ₀ sin 2 θ _ + A ₄ cos, 4 θ _ + B ₄ sin4 Q

(D

where the Fourier coefficients have the following form:

^A o = 2 ~ cos 2 2 Ψ Ψ A ₂ = O 2 ^B 2 = 2 sin Ψ sin Δ ^A 4 = - cos

B. = sin 2 ψ cosΔ

Since the intensity is only within a multiplicative constant j

I I

^{1 is} measured, it is only the ratios of the ¹ Fourier coefficients mentioned above that contain the information required to determine the test object parameters Ψ and Δ. It is therefore useful to divide each coefficient by an average intensity level through A _Q so that the following relationships hold true:

a ₂ = A ₂ / A _o = 0

^b 2 ^{= B} 2 / ^A 0 ^{= 2 sin 2 ψ sinA}

a ₄ = A./A = -cos 2 <p / (2-cos 2ψ) (4)

b ₄ = B ₄ / A _o = sin 2 ψ cosA / (2-cos 2ψ) (5)

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The equations (4) and (5) for Ψ and Δ can be | be solved:!

Ψ = 1/2 cos i-i-i / (6)

(7)

Δ =

a ₄ tan 2

'From the above equations will be described as shown by the' measurement of the intensity of the current through the combination of the of the rotating compensator 50 and the fixed analyzer 52 device as a function of Kompensatorazimuths θ _ transmitted light is a completely unambiguous determination of the polarization state of the incident light and thus the j unambiguous determination of the test object parameters Ψ and Δ for the purposes of ellipsometry is possible. The ambiguity occurring in the known ■ method is used in the case of the invention; A moderate method is avoided in that the intensity I ( q ) in the present case consists of a constant and two sinusoidal terms, while with the previously known methods only a single sinusoidal I term could be determined with the aid of the rotating analyzer. As can be seen from equation (1), i contains one of these sinusoidal components (β λ sin 4 q) four times the angular frequency of the compensator, whereby essentially the same information is obtained as with the device with the rotating analyzer, and sinusoidal terms; (A ₀ cos 2 0) and (B ₀ sin 2 Q), which contain twice the angular frequency ι. It should be noted that the last-mentioned J term changes its phase by 180 ° with a change in the polarization sense of the incident light. It follows that! the numerical Fourier analysis applied when using a rotating compensator can be used for the analysis of the intensity _{data! (8 C} ) which arise when a rotating compensator according to FIG. 4 is used.

YO 974 065 609 846/0 87

The advantages of the improved according to the present invention ^! Ellipsometric method can also be based on the equations

(2) to (7) will be explained. It can be shown that Ψ in a can be clearly determined, since it is always between 0

and 90 °, while Δ can take one of two values, since it is between 0 and 360. In the case of the present! Invention improved ellipsometry method, the additional information by the term b the illustrated ₂ for ^j: Value Δ be precisely defined, as a study shows that i the same sign as this term must have sinA. Since the

According to equation (7) two possible values of Δ opposite ^{: result in the} sign for b ₂ , the ambiguity of the sign of Δ is eliminated so that it defines it in an unambiguous manner

: In the device shown in Fig. 4 are through the ! Encryptor the same information as provided by the encryptor

■ ler 30, in the case of the FIGS. 1 and 2 shown device ' determined. The device shown in FIG. 4 rotates

the encryptor 30, however, together with the compensator 50,; so that the pulses occurring at the outputs 31 and 33 the j Define the rotation of the! Compensator 50, while in the ; Figs. 1 and 2, these pulses defined the rotation j of the analyzer 26. The one at the exit of the photo detector j 28 occurring signal is in the analog / digital converter 32 in digi-

' converted tal values, which then in the analyzer 38 a ι
Fourier analysis are carried out in order to determine the values δ and ψ in the manner described in the above-mentioned German Offenlegungsschrift 2,430,521.

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. ,,. 2616H1

In the embodiment described in Fig. 5, the rotating Compensator 50 arranged in the course of the incident beam between polarizer 12 and test object 20. With this embodiment the same results are achieved, but in the mathematical calculations the Azimuth angles of the polarizer 12 and the analyzer 52 with respect to to the analysis of the device according to FIG. 4 is reversed.

An ideal compensator was assumed for the calculations described above. However, it has been shown that in practice

j is the delay in the mutually perpendicular directions I only approximately equal to a quarter for all wavelengths j is wavelength. In addition, the transmissions of the two main axes show slight differences. With the known Ellipsometric methods make these inaccuracies two j manual null measurements are required to obtain the Abj to take into account deviations from an ideal compensator. In the method according to the present invention it is possible to dimension the device with the rotating compensator so that I these inaccuracies are compensated.

ι Due to the inaccuracies of the compensator mentioned, the

.measured values influenced as follows. The complex transmission!
ratio of the slow and fast compensator directions

let by the two compensator parameters Ψ and Δ (Ψ and Δ

C C

the test object parameters are defined as follows:

slow / ^T fast = ^tan 5 ^W c ^e "^ ^c < ^S)

where in the ideal case Ψ _c = 45 ° and Δ _c = 90 °. The coefficients of equation (1) are thus:

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A _n = 2 - (1 + sinΨ cos Δ) cos 2 Ψ

A _n = 2 cos 2Ψ (1 - cos 2Ψ)
2 c

B ^ = 2 sin 2 Ψ (cos 2 Ψ cos Δ + sin 2 Ψ sinΔ sinΔ)

Α _Λ = "(1 - sin 2 Ψ cosA) cos 2Ψ 4 cc

B. = (1 - sin 2 Ψ cos Δ) sin 2Ψ cosA

ri CC

The effect of the inaccuracies in the compensator can be harmless can be made by first characterizing the compensator to determine the corresponding values of Δ and W

C Car

will. This can be achieved, for example, by a measurement in which the front polarizer 12 (Fig. 4) outgoing light without previous reflection on a test object directly in the rotating compensator 50 arrives. Such an arrangement is the optical equivalent of a setting of Ψ = 45 ° and Δ = 0 and their detection in the above equations. so that the resulting coefficients for the adjustment measurement have the form:

^a 2 ^{= A} 2 ^{/ A} 0 ^{= COS 2} ^ c ⁽⁹⁾

b ₂ = B ₂ / A _o = cos 2 Ψ _α (10)

^a 4 ⁼ V ^A 0 ⁼ ° ^{11)

b ₄ = B ₄ / A _o = (1-sin 2 Ψ _ο cos h _Q ) / 2 (12)

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A resolution according to the compensator parameters results in:

Ψ = 1/2 cos ~ ¹ (a ₀ ) (should be approximately 45 °) (13)

Δ = cos' ¹ ((1-2b,) / sin 2 Ψ) (should be approximately

^{c 4 c} 90 ^ö be) (14)

There is also an experimental verification of this measurement, namely that a _{2 should} equal b ₂ and a ₄ equal 0. With the compensator characterized or calibrated in this way, the test object parameters for the non-ideal compensator can be determined using the equations

Ψ = 1/2 cos " ¹ (2a ₄ / aa ₄ - δ)) (15)

Δ = cos " ¹ (--b ₄ / a ₄ tan 2Ψ)) (1G)

α = 1 + sin 2Ψ cos Δ. (17)

c c

6 = 1- sin 2 Ψ cos Δ.
cc

The correct or compensated value for Δ of the two values permitted by equation (16) can be determined as before on the basis of the fourth of b “. It should be noted that equation (16) is identical to equation (7), which shows that the inaccuracies of the compensator only affect the values of the test object parameter U.

YO 974 065 6098 AB / 087 3

The present invention enables the method described in the above-mentioned German interpretation, by which the parameters Ψ and Δ can be determined at high speed for unambiguous values of 4 ·, by generating the sin Δ and cos Δ terms in two different ways Respect improved. First, the values of Δ become in the range wherejcosA | approximately ^; 1 is much more precisely detectable and, secondly, the values for A become unambiguous. In addition, it is possible to take account of errors in the! Compensator used in a computational manner.

Although in the previous calculations the symbols R and R

P ^s

only as the parallel and the perpendicular components of the electrical Vector of the elliptically polarized reflected beam and the ellipsometric parameters of the test object ψ and Δ were defined as functions of R and R where an angle

ο P ^s

of 45 was assumed between the plane of the linearly polarized light beam and the plane of incidence, the present one refers Invention to the general case of elliptically polarized incident and reflected light. In this case, the following relationships;

_ rp - ^E p

^R s = ^E s ^{/ E} s

where E ^ and E are the parallel and perpendicular components, respectively I s

of the elliptically polarized incident light beam,

rr
while E and E are the corresponding parallel and perpendicular components of the elliptically polarized reflected light beam. R and R are thus the reflection coefficients

P ^s
of the test object for parallel and perpendicular polarized light.

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The ellipsometric test object parameters Δ and Ψ are from R and R depend on the following equation:

R / R ₃ = tan ¹ ! *

In the general case described last, Δ is the phase difference between the parallel (R) and the vertical (R) Re--

ρ s

flexion coefficient of the test object., where V is defined by

tan, -

The vertical lines denote the absolute fourth of the complex ratio R / R with the help of the invention

P ^s
the values Ψ and Δ are clearly defined for the general case of elliptically polarized incident and reflected light.

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Claims (1)

PATENT CLAIMS Ellipsometric measuring method in which a polarized Light beam with a known angle of incidence and with a known position of its polarization direction directed onto a test object and after reflection at this is fed to an analyzer and a downstream photodetector, characterized in that a polarized light beam (21) before or after its reflection on a test object (20) a the relative phase position of the perpendicular to each other Components periodically changing element (50) penetrated, in the further course of an analyzer (52) and a Photodetector (28) is supplied, and that the signals occurring at the output of the photodetector together with the respective rotational position of the element (50), which periodically changes the relative phase position, signals a Analyzing device (38) for determining the Fourier coefficients is supplied, at the output of which the ellipsometric test object parameters ψ and Λ are generated. Method according to claim 1, characterized in that the Fourier coefficients of the function defined by the signals appearing at the output of the photodetector (28) are calculated to determine sinA, cosa and ψ, where 4 ^ er phase difference between each other vertical components R or R of the electrical P s _R tors of the reflected beam and tang Ψ = _ £. ^R s YO 974 065 609846/087 3 Method according to Claims 1 and 2, characterized in that to compensate for the errors of the phase position of the two components changing element (50) the errors of the parameters Ψ and Δ of this element c c can be determined at direct incidence of the polarized beam. Method according to one or more of the preceding claims, characterized in that the of the photodetector (28) occurring analog signals are digitized before their further processing. Device for carrying out the method according to Claims 1 to 4, characterized by a light source (10) for generating a monochromatic, incident on a test object at an adjustable angle Light beam (21), through one in the course of the light beam before it hits the test object (20) arranged polarizer (12), by a device for setting the azimuth angle of the polarizer in relation to the plane of incidence of the beam passing through it, by an analyzer (50) arranged in the path of the light beam (22) reflected on the test object (20), a this downstream photodetector (28), an analog-digital converter connected to the output (35) of the photodetector (32) and an analyzing device (38) connected downstream of this, as well as by one in the beam path of the light beam reflected on the test object Element (50) for periodically changing the relative phase position of the mutually perpendicular components of the light beam. YO 974 065 6098 46/087 3 Device for carrying out the method according to Claims 1 to 4, characterized by a light source
(10) for generating a monochromatic light beam (21) incident on a test object (20) at an adjustable angle, by a polarizer (12) arranged in the course of the light beam before it hits the test object (20), by a device for azimuth Angle adjustment of the polarizer in relation to the plane of incidence of the beam passing through it by an analyzer (52) arranged in the path of the light beam reflected on the test object, a downstream analyzer
Photodetector (28), an analog-digital converter (32) connected to the output (35) of the photodetector and an analyzing device (38) connected downstream of this, as well as
a through in the beam path of the light beam behind the
first polarizer (12) and, before it strikes the test object (20), arranged element (50) for periodically changing the relative phase position of the mutually perpendicular components of the light beam. 7. Device according to claims 5 or 6, characterized in that the relative phase position of each other
perpendicular components of the polarized light beam
periodically changing element (50) consists of a λ / 4 plate rotating around the central axis of the polarized light beam. ¥ 0 974 Ο65 6098 46/0873